10.8 Fundamental Counting Principal, Permutation & Combination

Determine whether the question would be a permutation or combination: Five students from 90 will be selected to count ballots for the Class President election. How many groups of 5 students could be selected to count ballots?

• Permutation

• Combination

• Neither

Permutation, combination, or neither?
Rob and Mary are planning trips to 9 countries this year.  There are 13 countries they would like to visit.  They are deciding which countries to skip.

• combination
• permutation
• neither

What does ₁₀P₅ mean?

• Permutations with 5 choices and 10 positions
• Permutations with 10 choices and 5 positions
• Permutations with 5 numbers and 10 operations
• Permutations with 5 hot dogs and 10 drinks

Is the order of arrangement important?
Find the number of ways to form a team of three players for a game out of a group of 10 individuals.

• Yes
• No

Determine whether the following scenarios are a permutation or a combination:
 
Selecting a lead and an understudy for a school play.

• Combination
• Permutation

In the orchestra, there are eight violinists in the front row. How many different ways can they be seated?

• 40320
• 1
• 64
• 8

The ski club with ten members is to choose three officers for captain, co-captain and secretary.  How many ways can those offices be filled?

• 720
• 120
• 10!

How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits?

• 90
• 6

• 12
• 24

A disc jockey has to choose three songs for the last few minutes of his evening show.  If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose to play three of those nine songs?

• 84
• 504
• 9!
• 3!

How would you solve?

Sarah plays softball over the summer.  If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?

• Permutation

• Counting Principles

• Factorial

• Combination